Animation of falling paper in cycles
You can use force fields to obtain this kind of effects, specially 'wind' and 'vortex'.



But I did not succeed the zigzag you mentioned

The paper is a soft body, with no particular parameters. 

Then add some force fields and tune them..., for instance this kind of configuration, where :


Strength and flow allows to create an air flow at the given strength
Noise and seed add some randomness to the flow
Power and min/max defines a falloff of the field






I don't know if the zigzag is possible with a paper in real.. but anyway, as said before, I did not succeed to turn that into a zigzag...  

Hope this help however.